document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=847501>Question 847501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is there a real number for x such that- \r<BR>\n" );
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document.write( "cosec(x) = sin(1/x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #510488 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=510488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> csc(x) = sin(1/x)\r<BR>\n" );
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document.write( "1/sin(x) = sin(1/x)\r<BR>\n" );
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document.write( "This implies that 1 = sin(x) * sin(1/x)\r<BR>\n" );
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document.write( "Since sin(x) ranges from -1 to 1 and sin(1/x) ranges from -1 to 1, the only possible multiplication is if sin(x)= 1 and sin(1/x)= 1\r<BR>\n" );
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document.write( "Well if sin(x) = 1, then we find x = pi/2 or 90 degrees.\r<BR>\n" );
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document.write( "However when we plug this same x value back into sin(1/x):\r<BR>\n" );
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document.write( "sin(2/pi) does not = 1. It equals .594.\r<BR>\n" );
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document.write( "Since our only possible situation did not pan out, it is safe to assume that there is NO SOLUTION that satisfies this.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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